Math Problem Statement

Solve this

Solve each equation from the image provided.

Solution

I can see the math problems in the image you uploaded. Let's solve them one by one:

1. 4n2n=44n - 2n = 4

2n=4    n=42=22n = 4 \implies n = \frac{4}{2} = 2 Solution: n=2n = 2


2. 12=2+5v+2v-12 = 2 + 5v + 2v

12=2+7v    122=7v    14=7v    v=147=2-12 = 2 + 7v \implies -12 - 2 = 7v \implies -14 = 7v \implies v = \frac{-14}{7} = -2 Solution: v=2v = -2


3. 3=x+35x3 = x + 3 - 5x

3=4x+3    33=4x    0=4x    x=03 = -4x + 3 \implies 3 - 3 = -4x \implies 0 = -4x \implies x = 0 Solution: x=0x = 0


4. x+33=6x + 3 - 3 = -6

x=6x = -6 Solution: x=6x = -6


5. 12=32k3k-12 = 3 - 2k - 3k

12=35k    123=5k    15=5k    k=155=3-12 = 3 - 5k \implies -12 - 3 = -5k \implies -15 = -5k \implies k = \frac{-15}{-5} = 3 Solution: k=3k = 3


6. 1=3r+2r-1 = -3r + 2r

1=r    r=1-1 = -r \implies r = 1 Solution: r=1r = 1


7. 6=3(x+2)6 = -3(x + 2)

6=3x6    6+6=3x    12=3x    x=123=46 = -3x - 6 \implies 6 + 6 = -3x \implies 12 = -3x \implies x = \frac{12}{-3} = -4 Solution: x=4x = -4


8. 3(4r8)=36-3(4r - 8) = -36

12r+24=36    12r=3624    12r=60    r=6012=5-12r + 24 = -36 \implies -12r = -36 - 24 \implies -12r = -60 \implies r = \frac{-60}{-12} = 5 Solution: r=5r = 5


9. 24=6(x3)24 = 6(-x - 3)

24=6x18    24+18=6x    42=6x    x=426=724 = -6x - 18 \implies 24 + 18 = -6x \implies 42 = -6x \implies x = \frac{42}{-6} = -7 Solution: x=7x = -7


10. 75=3(6n5)75 = 3(6n - 5)

75=18n15    75+15=18n    90=18n    n=9018=575 = 18n - 15 \implies 75 + 15 = 18n \implies 90 = 18n \implies n = \frac{90}{18} = 5 Solution: n=5n = 5


Feel free to ask for further explanations or details on any of these steps. Would you like a detailed breakdown of any solution?

Here are 5 relative questions:

  1. What is the process for solving linear equations?
  2. Can you explain how to solve equations with variables on both sides?
  3. How do you handle equations with negative coefficients?
  4. What is the importance of checking your solution by substituting back into the equation?
  5. How can solving multi-step equations help in real-life situations?

Tip: Always combine like terms first to simplify equations before solving for the variable.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Simplification
Variable Isolation

Formulas

Basic linear equation: ax + b = c

Theorems

Distributive Property
Combining Like Terms

Suitable Grade Level

Grades 6-8